Can someone explain PTEX mapping and how to use it in Blender?
You can not use it in Blender with Cycles neither internal, it is not supported yet.  Also you can not show them in viewport in Blender. Renderman supports it as PTEX is Disney product.

A Ptex file is an image file format, it isn't a purely 2d file format, but contains 2d pixel information on a face by face basis for a 3d model. So you can use it to avoid UV mapping. In nutshell it stores texture for every face.

It has some disadvantages though. Some of them are: 


Some things are just easier to paint in 2d.
No photoshop support. Photoshop is the most common tool for painting textures in the industry, but it does not allow you to paint on Ptex files.
Changing the geometry of the model (like adding or deleting faces or edges) requires you to bake the Ptex file from the old geometry to your new geometry with possible quality loss. This is a solvable problem, Mudbox for example has the ability to transfer ptex from one model to another. But it is an extra step you have to worry about.
Ptex files are generally associated with their corresponding object by name, so Hand01.ptx is assigned to the 3d object in your scene called Hand01. So if you rename your model, you also need to rename its corresponding Ptex file.
Again, since ptex are associated to their object by object name, if you have 200 objects that need an identical color map, its easier to do that using uvs than to create and maintain 200 identical ptex files that are named for each object.


I think that industry will still keep UV especially with UDIM support before PTEX.